Abstract : Flow fields with vortex separation play an important role in the aerodynamics of missiles and for airplanes. Investigations carried out recently have shown that such flow fields can be computed by means of solutions of the Euler-equations. In the present paper results are presented for flow fields around delta-wings with freestream Mach number larger than 1. The range of the angle of attack is up to a = 15 deg. The Euler-equations are integrated by using a space-marching finite-difference method. The delta-wings have got sharp and blunted leading edges. At the sharp leading edge a condition is prescribed which produces a tangential discontinuity by means of which vorticity is introduced into the flow field. The formulation of the governing equations, the boundary conditions and the initial data is discussed. The results shown are the contours of the bow shock, the isobars, the lines of constant total pressure and the velocity vectors of the cross flow. The wave drag is determined by evaluating the integral relation for the momentum in an adequate surface in the flow field. (Author)